Problem 43 - Prealgebra

Question

Add the following numbers left to right. $$-321+752+(-324)$$

Step-by-Step Solution

Answer

The sum of the numbers is 107.

Step 1: Add the first two numbers

Start by adding the first two numbers in the sequence: \(-321 + 752\). To do this, subtract 321 from 752, because adding a negative number is the same as subtraction. \(752 - 321 = 431\). Thus, the result of adding the first two numbers is 431.

Step 2: Add the result to the next number

Take the result from Step 1, which is 431, and add it to the next number in the sequence: \(431 + (-324)\). Adding a negative number is the same as subtracting it:\(431 - 324 = 107\). Thus, the final result after all additions is 107.

Key Concepts

Negative Numbers

Negative numbers are values that are less than zero. They are commonly used in mathematics to represent a shortage or a deficit. For example, if you have a debt of $5, your account balance can be represented as -5 dollars. It is vital to understand that negative numbers can be found in various applications from temperature scales to financial transactions.

When dealing with operations that include both negative and positive numbers, the sign of the number can significantly change the result. For example:

• Positive + Positive = Positive
• Negative + Negative = More Negative
• Positive + Negative = Depends on their values

These simple rules allow you to predict the general outcome when adding numbers of different signs, and will help you navigate through more complex problems.

Sequential Addition

Sequential addition involves adding numbers in a specific order. This is useful because you only handle two numbers at a time, making the process simpler and more organized. Let's say you have a sequence of numbers to add: when performing sequential addition, you start with the first two numbers, find their sum, and then add the next number to the result.

In the exercise, the sequence was -321 + 752 + (-324).
Starting with the first two numbers:

• Add -321 and 752

You get 431. Then, you take this result and add it to the third number:

• Add 431 and -324

This results in 107. By following this approach, you ensure that each step is manageable, preventing mistakes that often occur when handling all numbers at once.

Subtraction as Addition of Negatives

Subtraction is often better understood by rethinking it as adding a negative number. This interpretation helps in keeping mathematical operations into a single form: addition.

For example, if you have the expression like 5 - 3, think of it as 5 + (-3), because subtracting 3 is equivalent to adding a negative 3.

• This method is especially helpful while dealing with multiple operations in a sequence, as it reduces complexity.
• It also aligns well with rules of integer addition, where adding negatives is intuitive once you grasp the basic concepts mentioned first.

In our exercise, add -324 was substituted as subtract 324. This substitution helped simplify the addition process and ensured accurate results.